CRUCIAL THEOREM IN THERMODYNAMICS

Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can
be assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev

Pentcho Valev wrote:
Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can
be assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev

On May 6, 3:13*am, Pentcho Valev wrote:
Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu *= *(dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu *and *(dFk/dLu)_Lk can
be assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev


You mean, there are actually people who are passionate about the
second law of thermodynamics?... You know, when I took that class, you
were lucky if you didn't drop dead from boredom... and the professor
had questions about the big bang theory in his test questions...
Whatever.

Pentcho Valev wrote:
Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can
be assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev

Pentcho Valev wrote:
Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can
be assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev

Originally, the second law of thermodynamics appeared in 1824 as the
conclusion in an argument advanced by Carnot:

Premise 1: Heat is an indestructible substance (cannot be converted
into work in the heat engine).
Premise 2: Perpetuum mobile of the first kind is impossible.
Conclusion: All heat engines working reversibly between the same two
temperatures have the same efficiency.

Carnot's 1824 argument was valid but Premise 1 turned out to be false
in the end (in fact, heat IS converted into work in the heat engine).
The crucial question:

How can a FALSE premise be indispensable in the deduction of a TRUE
conclusion?

has never been asked. (Those who would think that Premise 1 was not
indispensable for Carnot's argument should try to deduce the
conclusion from Premise 2 alone).

Let me advance a hypothesis: If the crucial question had been both
asked and answered, the following sad texts would never have been
written:

http://www.guardian.co.uk/science/20.../22/schools.g2
"We are nearing the end of the "World Year of Physics", otherwise
known as Einstein Year, as it is the centenary of his annus mirabilis
in which he made three incredible breakthroughs, including special
relativity. In fact, it was 100 years ago yesterday that he published
the most famous equation in the history of physics: E=mc2. But instead
of celebrating, physicists are in mourning after a report showed a
dramatic decline in the number of pupils studying physics at school.
The number taking A-level physics has dropped by 38% over the past 15
years, a catastrophic meltdown that is set to continue over the next
few years. The report warns that a shortage of physics teachers and a
lack of interest from pupils could mean the end of physics in state
schools. Thereafter, physics would be restricted to only those
students who could afford to go to posh schools. Britain was the home
of Isaac Newton, Michael Faraday and Paul Dirac, and Brits made world-
class contributions to understanding gravity, quantum physics and
electromagnetism - and yet the British physicist is now facing
extinction. But so what? Physicists are not as cuddly as pandas, so
who cares if we disappear?"

http://www.guardian.co.uk/science/20...tion.education
Harry Kroto: "The wrecking of British science....The scientific method
is based on what I prefer to call the inquiring mindset. It includes
all areas of human thoughtful activity that categorically eschew
"belief", the enemy of rationality. This mindset is a nebulous mixture
of doubt, questioning, observation, experiment and, above all,
curiosity, which small children possess in spades. I would argue that
it is the most important, intrinsically human quality we possess, and
it is responsible for the creation of the modern, enlightened portion
of the world that some of us are fortunate to inhabit. Curiously, for
the majority of our youth, the educational system magically causes
this capacity to disappear by adolescence.....Do I think there is any
hope for UK? I am really not sure."

Pentcho Valev wrote:

Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can be
assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev

Lakatos' protective belt consists of ad hoc auxiliary hypotheses which
protect false premises against experimental falsification. So the ad
hoc hypothesis that moving bodies contract, introduced by FitzGerald
and Lorentz, converted the Michelson-Morley experiment proving that
the speed of light does depend on the speed of the emitter into an
experiment proving that the speed of light does not depend on the
speed of the emitter.

In 1850 Clausius did something different: he sacrificed Carnot's false
premise but protected the precious conclusion against logical
falsification by introducing an AD HOC AUXILIARY ARGUMENT where the
precious conclusion allegedly follows from another premise, true this
time:

http://web.lemoyne.edu/~giunta/Clausius.html
"Ueber die bewegende Kraft der Warme" 1850 Rudolf Clausius: "Carnot
assumed, as has already been mentioned, that the equivalent of the
work done by heat is found in the mere transfer of heat from a hotter
to a colder body, while the quantity of heat remains undiminished. The
latter part of this assumption--namely, that the quantity of heat
remains undiminished--contradicts our former principle, and must
therefore be rejected... (...) It is this maximum of work which must
be compared with the heat transferred. When this is done it appears
that there is in fact ground for asserting, with Carnot, that it
depends only on the quantity of the heat transferred and on the
temperatures t and tau of the two bodies A and B, but not on the
nature of the substance by means of which the work is done. (...) If
we now suppose that there are two substances of which the one can
produce more work than the other by the transfer of a given amount of
heat, or, what comes to the same thing, needs to transfer less heat
from A to B to produce a given quantity of work, we may use these two
substances alternately by producing work with one of them in the above
process. At the end of the operations both bodies are in their
original condition; further, the work produced will have exactly
counterbalanced the work done, and therefore, by our former principle,
the quantity of heat can have neither increased nor diminished. The
only change will occur in the distribution of the heat, since more
heat will be transferred from B to A than from A to B, and so on the
whole heat will be transferred from B to A. By repeating these two
processes alternately it would be possible, without any expenditure of
force or any other change, to transfer as much heat as we please from
a cold to a hot body, and this is not in accord with the other
relations of heat, since it always shows a tendency to equalize
temperature differences and therefore to pass from hotter to colder
bodies."

Pentcho Valev wrote:

Originally, the second law of thermodynamics appeared in 1824 as the
conclusion in an argument advanced by Carnot:

Premise 1: Heat is an indestructible substance (cannot be converted
into work in the heat engine).
Premise 2: Perpetuum mobile of the first kind is impossible.
Conclusion: All heat engines working reversibly between the same two
temperatures have the same efficiency.

Carnot's 1824 argument was valid but Premise 1 turned out to be false
in the end (in fact, heat IS converted into work in the heat engine).
The crucial question:

How can a FALSE premise be indispensable in the deduction of a TRUE
conclusion?

has never been asked. (Those who would think that Premise 1 was not
indispensable for Carnot's argument should try to deduce the
conclusion from Premise 2 alone).

Let me advance a hypothesis: If the crucial question had been both
asked and answered, the following sad texts would never have been
written:

http://www.guardian.co.uk/science/20.../22/schools.g2
"We are nearing the end of the "World Year of Physics", otherwise
known as Einstein Year, as it is the centenary of his annus mirabilis
in which he made three incredible breakthroughs, including special
relativity. In fact, it was 100 years ago yesterday that he published
the most famous equation in the history of physics: E=mc2. But instead
of celebrating, physicists are in mourning after a report showed a
dramatic decline in the number of pupils studying physics at school.
The number taking A-level physics has dropped by 38% over the past 15
years, a catastrophic meltdown that is set to continue over the next
few years. The report warns that a shortage of physics teachers and a
lack of interest from pupils could mean the end of physics in state
schools. Thereafter, physics would be restricted to only those
students who could afford to go to posh schools. Britain was the home
of Isaac Newton, Michael Faraday and Paul Dirac, and Brits made world-
class contributions to understanding gravity, quantum physics and
electromagnetism - and yet the British physicist is now facing
extinction. But so what? Physicists are not as cuddly as pandas, so
who cares if we disappear?"

http://www.guardian.co.uk/science/20...tion.education
Harry Kroto: "The wrecking of British science....The scientific method
is based on what I prefer to call the inquiring mindset. It includes
all areas of human thoughtful activity that categorically eschew
"belief", the enemy of rationality. This mindset is a nebulous mixture
of doubt, questioning, observation, experiment and, above all,
curiosity, which small children possess in spades. I would argue that
it is the most important, intrinsically human quality we possess, and
it is responsible for the creation of the modern, enlightened portion
of the world that some of us are fortunate to inhabit. Curiously, for
the majority of our youth, the educational system magically causes
this capacity to disappear by adolescence.....Do I think there is any
hope for UK? I am really not sure."

Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can be
assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev

spam

Over the years the second law of thermodynamics took numerous
monstrous forms, e.g. this one:

L. McGlashan, Chemical thermodynamics, Academic Press, London (1979),
pp. 72-73:
"For an infinitesimal change in the state of a phase alpha we write
dU = T dS - p dV + SUM mu_B dn_B (1)
We regard equation (1) as an axiom and call it the fundamental
equation for a change of the state of a phase alpha. It is one half of
the second law of thermodynamics. We do not ask where it comes from.
Indeed we do not admit the existence of any more fundamental relations
from which it might have been derived. Nor shall we here enquire into
the history of its formulation, though that is a subject of great
interest to the historian of science. It is a starting point ; it must
be learnt by heart. It may be allowed to stand as an axiom until any
single one of the host of equations that can be derived from it (with
the help of other axioms of thermodynamics) has been shown
experimentally to be false."

In other words, thermodynamics simply died. The last major
"development" took place 60-70 years ago and can be described as
follows:

For a closed system doing reversible work of expansion the first law
of thermodynamics takes the form

dU = dQ - PdV /1/

where dU is the internal energy change, dQ is the heat absorbed, P is
pressure and V is volume. Since the system is CLOSED and undergoes
reversible changes the entropy change is, by definition, dS=dQ/T and /
1/ becomes:

dU = TdS - PdV /2/

J. Gibbs had managed to convince the world that, if the system is OPEN
(substances are added to it), /2/ should be replaced by the equation:

dU = TdS - PdV + SUM mu_i dn_i /3/

where mu_i is the chemical potential and n_i is the amount of the ith
component. However Gibbs had failed to explain the meaning of the
entropy change, dS, for an OPEN system. Is dS again equal to dQ/T, as
it is for a closed system, or is dS equal to something else now that a
procedure as drastic as the addition of substances to the system is
introduced?

The fact that dS was not defined for open systems made the equation /
3/ so fashionable (scientists adore equations with undefined terms)
that in the end /3/ was called "the fundamental equation of
thermodynamics". Yet scientists somehow felt that a new explicit
definition of dS could bring even more career and money. The quickest
among them, Ilya Prigogine, simply combined /1/ and /3/ and obtained

dS = dQ/T - (1/T)SUM mu_i dn_i /4/

That was a new incredible definition of the entropy change (the
scientific community had never seen anything like that) so the Nobel
Committee immediately gave Prigogine the Nobel prize.

Believers do not know how /4/ can be "shown experimentally to be
false". Similarly, they do not know how the statement "The greenness
of the crocodile exceeds its length" can be shown experimentally to be
false.

Pentcho Valev wrote:

Lakatos' protective belt consists of ad hoc auxiliary hypotheses which
protect false premises against experimental falsification. So the ad
hoc hypothesis that moving bodies contract, introduced by FitzGerald
and Lorentz, converted the Michelson-Morley experiment proving that
the speed of light does depend on the speed of the emitter into an
experiment proving that the speed of light does not depend on the
speed of the emitter.

In 1850 Clausius did something different: he sacrificed Carnot's false
premise but protected the precious conclusion against logical
falsification by introducing an AD HOC AUXILIARY ARGUMENT where the
precious conclusion allegedly follows from another premise, true this
time:

http://web.lemoyne.edu/~giunta/Clausius.html
"Ueber die bewegende Kraft der Warme" 1850 Rudolf Clausius: "Carnot
assumed, as has already been mentioned, that the equivalent of the
work done by heat is found in the mere transfer of heat from a hotter
to a colder body, while the quantity of heat remains undiminished. The
latter part of this assumption--namely, that the quantity of heat
remains undiminished--contradicts our former principle, and must
therefore be rejected... (...) It is this maximum of work which must
be compared with the heat transferred. When this is done it appears
that there is in fact ground for asserting, with Carnot, that it
depends only on the quantity of the heat transferred and on the
temperatures t and tau of the two bodies A and B, but not on the
nature of the substance by means of which the work is done. (...) If
we now suppose that there are two substances of which the one can
produce more work than the other by the transfer of a given amount of
heat, or, what comes to the same thing, needs to transfer less heat
from A to B to produce a given quantity of work, we may use these two
substances alternately by producing work with one of them in the above
process. At the end of the operations both bodies are in their
original condition; further, the work produced will have exactly
counterbalanced the work done, and therefore, by our former principle,
the quantity of heat can have neither increased nor diminished. The
only change will occur in the distribution of the heat, since more
heat will be transferred from B to A than from A to B, and so on the
whole heat will be transferred from B to A. By repeating these two
processes alternately it would be possible, without any expenditure of
force or any other change, to transfer as much heat as we please from
a cold to a hot body, and this is not in accord with the other
relations of heat, since it always shows a tendency to equalize
temperature differences and therefore to pass from hotter to colder
bodies."

Originally, the second law of thermodynamics appeared in 1824 as the
conclusion in an argument advanced by Carnot:

Premise 1: Heat is an indestructible substance (cannot be converted
into work in the heat engine).
Premise 2: Perpetuum mobile of the first kind is impossible.
Conclusion: All heat engines working reversibly between the same two
temperatures have the same efficiency.

Carnot's 1824 argument was valid but Premise 1 turned out to be false
in the end (in fact, heat IS converted into work in the heat engine).
The crucial question:

How can a FALSE premise be indispensable in the deduction of a TRUE
conclusion?

has never been asked. (Those who would think that Premise 1 was not
indispensable for Carnot's argument should try to deduce the
conclusion from Premise 2 alone).

Let me advance a hypothesis: If the crucial question had been both
asked and answered, the following sad texts would never have been
written:

http://www.guardian.co.uk/science/20.../22/schools.g2
"We are nearing the end of the "World Year of Physics", otherwise
known as Einstein Year, as it is the centenary of his annus mirabilis
in which he made three incredible breakthroughs, including special
relativity. In fact, it was 100 years ago yesterday that he published
the most famous equation in the history of physics: E=mc2. But instead
of celebrating, physicists are in mourning after a report showed a
dramatic decline in the number of pupils studying physics at school.
The number taking A-level physics has dropped by 38% over the past 15
years, a catastrophic meltdown that is set to continue over the next
few years. The report warns that a shortage of physics teachers and a
lack of interest from pupils could mean the end of physics in state
schools. Thereafter, physics would be restricted to only those
students who could afford to go to posh schools. Britain was the home
of Isaac Newton, Michael Faraday and Paul Dirac, and Brits made world-
class contributions to understanding gravity, quantum physics and
electromagnetism - and yet the British physicist is now facing
extinction. But so what? Physicists are not as cuddly as pandas, so
who cares if we disappear?"

http://www.guardian.co.uk/science/20...tion.education
Harry Kroto: "The wrecking of British science....The scientific method
is based on what I prefer to call the inquiring mindset. It includes
all areas of human thoughtful activity that categorically eschew
"belief", the enemy of rationality. This mindset is a nebulous mixture
of doubt, questioning, observation, experiment and, above all,
curiosity, which small children possess in spades. I would argue that
it is the most important, intrinsically human quality we possess, and
it is responsible for the creation of the modern, enlightened portion
of the world that some of us are fortunate to inhabit. Curiously, for
the majority of our youth, the educational system magically causes
this capacity to disappear by adolescence.....Do I think there is any
hope for UK? I am really not sure."

Kelvin's version of the second law of thermodynamics: It is impossible
to perform a cyclic process with no other result than that heat is
absorbed from a reservoir, and work is performed.

THEOREM: Kelvin's version of the second law is true if and only if,
whenever two INTERACTING heat engines absorb heat from a reservoir
(the surroundings) and perform reversible work, the following equality
of partial derivatives holds:

(dF1 / dX2)_X1 = (dF2 / dX1)_X2

where "d" is the sign for partial derivative, F1 and F2 are work-
producing forces and X1 and X2 are the respective displacements. If
the two partial derivatives are not equal, the second law is false.

Consider INTERACTING "chemical springs". There are two types of
macroscopic contractile polymers which on acidification (decreasing
the pH of the system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028
Dan W. Urry, "Physical Chemistry of Biological Free Energy
Transduction As Demonstrated by Elastic Protein-Based Polymers"

Polymers designed by Urry (U) absorb protons on stretching (as their
length, Lu, increases), whereas polymers designed by Katchalsky (K)
release protons on stretching (as their length, Lk, increases). (See
discussion on p. 11020 in Urry's paper).

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, if the
second law is true, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can be
assessed from experimental results reported on p. 11020 in Urry's
paper. As K is being stretched (Lk increases), it releases protons,
the pH decreases and, accordingly, Fu must increase. Therefore, (dFu/
dLk)_Lu is positive. In contrast, as U is being stretched (Lu
increases), it absorbs protons, the pH increases and Fk must decrease.
Therefore, (dFk/dLu)_Lk is negative.

One partial derivative is positive, the other negative: this proves
that the second law of thermodynamics is false.

Pentcho Valev

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